Question
A meteorologist claims that the average daily high temperature in Oklahoma City is \( 90^{\circ} \mathrm{F} \). Let \( \mu \) represent the average daily high temperature, in \( { }^{\circ} \mathrm{F} \), in Oklahoma City during the summer. What is the null hypothesis, \( H_{0} \), for this situation? \( \mu<90 \) \( \mu=90 \) \( \mu>90 \) \( \mu \geq 90 \) DONE
Ask by Zimmerman Whittaker. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The null hypothesis is \( \mu = 90 \)°F.
Solution
The meteorologist’s claim is that the average daily high temperature is 90°F. In hypothesis testing, the null hypothesis (H₀) typically represents the claim to be tested and is stated in the form of an equality. Therefore, the appropriate null hypothesis is:
H₀: μ = 90°F.
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Simplify this solution Extra Insights
The null hypothesis, \( H_{0} \), is typically a statement of no effect or no difference, and in this case, it serves as a baseline to compare against. Therefore, the correct null hypothesis here would be that the average daily high temperature in Oklahoma City is exactly \( 90^{\circ} \mathrm{F} \), denoted as \( H_{0}: \mu = 90 \). In hypothesis testing, rejecting the null hypothesis suggests that there is sufficient statistical evidence to support an alternative claim. Remember, the null hypothesis assumes that any variation observed is due to chance. So, if scientists find evidence otherwise, it could lead to some exciting discoveries about weather patterns!
